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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 362985, 10 pages
Research Article

The Existence and Uniqueness Result for a Relativistic Nonlinear Schrödinger Equation

Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, China

Received 3 August 2013; Revised 15 December 2013; Accepted 17 December 2013; Published 16 January 2014

Academic Editor: Bernhard Ruf

Copyright © 2014 Yongkuan Cheng and Jun Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the existence and uniqueness of positive solutions for a class of quasilinear elliptic equations. This model has been proposed in the self-channeling of a high-power ultrashort laser in matter.